Kinematics Equation Solver
Fill in any three of displacement, initial velocity, final velocity, acceleration, and time. Get the other two, in the units you want, with every step shown.
Most motion problems in physics class come down to picking the right one of five equations. This solver picks it for you, shows the substitution, and handles the tricky cases: unit conversions like km/h to m/s, a thrown ball that passes the same height twice, and numbers that can’t actually happen.
Leave the two you want to find blank. Choose one direction as positive and stick to it: anything pointing the other way is negative, including acceleration when an object slows down.
The five equations, and common mistakes
Each equation leaves out one of the five quantities. Find the one that skips the quantity you weren’t given and don’t need:
- These only work when acceleration is constant. If a problem has two stages (speeds up, then coasts), solve each stage separately. The final velocity of stage one is the initial velocity of stage two.
- Signs are where most points are lost. “Slows down” means acceleration points against the motion, so it gets the opposite sign from the velocity. For anything thrown or dropped, if up is positive then a = −9.8 m/s², and a fall of 45 m is s = −45 m.
- Hidden givens. “Starts from rest” means u = 0. “Comes to a stop” means v = 0. “At the top of its path” means v = 0 at that moment.
- Convert units first. Divide km/h by 3.6 to get m/s. This tool converts for you, and shows the SI values it used in the steps.
- Two answers? When you solve for time with v² = u² + 2as, a thrown object can reach the same height on the way up and on the way down. The tool shows both and drops any answer that needs negative time.
- Some textbooks use different letters: Δx or d for s, v0 or vi for u, and vf for v. The math is the same.
Everything runs in your browser. Your last problem is saved on this device only.